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OverviewFuchsian Reduction is a method for explicitly representing solutions of nonlinear PDEs near singularities. The technique has multiple applications in soliton theory, Einstein's equations and cosmology, stellar models, laser collapse, conformal geometry and combustion. Developed in the 1990s for semilinear wave equations, Fuchsian Reduction research has grown in response to those problems in pure and applied mathematics, where numerical computations fail. The exposition unfolds systematically in four parts, with theory and applications nicely interwoven. The methods used in various applications examined in Part III may serve as prototypes for future new applications. Background results in weighted Sobolev and Holder spaces as well as Nash--Moser implicit function theorem are provided. Most chapters contain a problem section and notes with references to the literature. This volume can be used as a text in graduate courses in PDEs and/or Algebra or as a resource for researchers working with applications to Fuchsian Reduction. Full Product DetailsAuthor: Satyanad KichenassamyPublisher: Birkhauser Boston Inc Imprint: Birkhauser Boston Inc Edition: 2007 ed. Volume: 71 Dimensions: Width: 15.50cm , Height: 1.90cm , Length: 23.50cm Weight: 0.625kg ISBN: 9780817643522ISBN 10: 0817643524 Pages: 289 Publication Date: 18 September 2007 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsFuchsian Reduction.- Formal Series.- General Reduction Methods.- Theory of Fuchsian Partial Di?erential Equations.- Convergent Series Solutions of Fuchsian Initial-Value Problems.- Fuchsian Initial-Value Problems in Sobolev Spaces.- Solution of Fuchsian Elliptic Boundary-Value Problems.- Applications.- Applications in Astronomy.- Applications in General Relativity.- Applications in Differential Geometry.- Applications to Nonlinear Waves.- Boundary Blowup for Nonlinear Elliptic Equations.- Background Results.- Distance Function and Hoelder Spaces.- Nash-Moser Inverse Function Theorem.ReviewsFrom the reviews: Fuchsian reduction is an analytical method to represent solutions to non-linear PDEs near singularities ... . The book under review provides a careful and instructive introduction into this method. ... At the end of most of the chapters some problems are posed, which are solved in an appendix. In total this is a highly interesting book containing a lot of original ideas and which suggests new developments. (R. Steinbauer, Monatshefte fur Mathematik, Vol. 158 (3), November, 2009) From the reviews: Fuchsian reduction is an analytical method to represent solutions to non-linear PDEs near singularities ... . The book under review provides a careful and instructive introduction into this method. ... At the end of most of the chapters some problems are posed, which are solved in an appendix. In total this is a highly interesting book containing a lot of original ideas and which suggests new developments. (R. Steinbauer, Monatshefte fur Mathematik, Vol. 158 (3), November, 2009) Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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